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arXiv:1201.3144 · Physical Review A

Disorder effects on the quantum coherence of a many-boson system

Zhihai Zhang, Pei Lu, Shiping Feng, Shi-Jie Yang

Published Mar 13, 2012• 5 citations
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Abstract

The effects of disorder on the quantum coherence for many-boson systems are studied in a double-well model. For the ground state, the disorder enhances the quantum coherence. In the deep Mott regime, dynamical evolution reveals periodical collapses and revivals of the quantum coherence, which is robust against the disorder. The average over variations in both the on-site energy and the interaction reveals a beat phenomenon of the coherence-decoherence oscillation in the temporal evolution.

DOI
10.1103/physreva.85.033617

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The effects of disorder on the quantum coherence for many-boson systems are studied in a double-well model. For the ground state, the disorder enhances the quantum coherence. In the deep Mott regime, dynamical evolution reveals periodical collapses and revivals of the quantum coherence, which is robust against the disorder. The average over variations in both the on-site energy and the interaction reveals a beat phenomenon of the coherence-decoherence oscillation in the temporal evolution.
The impurity effects on the quantum coherence of a few-boson system are studied within the two-site Hubbard model. Periodical collapses and revivals of coherence occur in the presence of either polarized or unpolarized fermionic impurities. The relative strength UBF/UBBU_{BF}/U_{BB}UBF​/UBB​ of the boson-fermion versus the boson-boson interactions plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for UBF/UBB=zU_{BF}/U_{BB}=zUBF​/UBB​=z (z∈Zz\in Zz∈Z is an integer) while the odd revival peaks are damped for UBF/UBB=z+1/2U_{BF}/U_{BB}=z+1/2UBF​/UBB​=z+1/2, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.
The impurity effects on the quantum coherence of a few-boson system are studied within the two-site Hubbard model. Periodical collapses and revivals of coherence occur in the presence of either polarized or unpolarized fermionic impurities. The relative strength UBF/UBB{U}_{BF}/{U}_{BB}UBF​/UBB​ of the boson-fermion interaction versus the boson-boson interaction plays a key role in the coherence revivals. As the average filling of the impurity increases, the coherence revivals remain nearly unaffected for UBF/UBB=z{U}_{BF}/{U}_{BB}=zUBF​/UBB​=z ($z\ensuremath{\in}Z$ is an integer) while the odd revival peaks are damped for UBF/UBB=z+1/2{U}_{BF}/{U}_{BB}=z+1/2UBF​/UBB​=z+1/2, in agreement with the experimental observations. For unpolarized fermionic impurities, the coherence revivals are irrelevant to the strength of the fermion-fermion interactions.
We study the quantum dynamics of cold Bose atoms in a double well. It is shown that self-trapping as well as population oscillations are common phenomena associated with nonlinear interactions. For larger U/tU/tU/t, multiparticle tunneling is damped and the quantum dynamics is dominated by single-particle tunneling. The many-body system can be effectively described in a truncated Fock space. It exhibits coherence-decoherence oscillations in the temporal evolution. We predict an interesting phenomenon of dynamical revival and collapse of matter wave fields in optical lattices in regimes near the superfluid--Mott-insulator phase boundary.
We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find a ``two negatives make a positive'' effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.
We explore the consequences of disorder on phase coherence in the Mott insulator phases in an optical lattice. Few bosons with contact interaction in small optical lattice can feature varieties of insulating phases---weakly interacting Mott in deep lattice, maximally fragmented and strongly interacting Mott in intermediate lattice, weak Mott with double filling and intrawell coherence, fermionized Mott with strong intrawell coherence. Utilization of the multiconfigurational time-dependent Hartree method for bosons to solve the many-boson Schr\"odinger equation, facilitates to understand the microscopic effect of disorder on the different kinds of Mott phases in the primary lattice. The many-body properties are analyzed by distinct measures of the reduced one-body density in real and momentum space, fragmentation, order parameter, variance of spatial single-shot measurements, compressibility, and the Glauber normalized correlation functions. We find very complex competition of localization due to disorder and Mott correlation. We observe distinct response of four different Mott phases in the disordered lattice. When the weakly interacting Mott exhibits the Bose glass phase, the strongly correlated and fully fragmented Mott exhibits leakage, melting and central localization. In contrast, weak Mott with double filling which is a spatially separated dimer in each site, exhibits only some dissociation of intrawell coherence and assist in the development of interwell coherence in the presence of strong disorder. For the fermionized Mott, when the density in each well is fragmented, strong disorder interferes with the intrawell correlation and the characteristic dip in each site starts to disappear leading to simple Mott localization with a pair of bosons.
We address the effects of quenched disorder averaging in the time-evolution of systems of ultracold atoms in optical lattices in the presence of noise, imposed by of an environment. For bosonic systems governed by the Bose-Hubbard Hamiltonian, we quantify the response of disorder in Hamiltonian parameters in terms of physical observables, including bipartite entanglement in the ground state and report the existence of disorder-induced enhancement in weakly interacting cases. For systems of two-species fermions described by the Fermi-Hubbard Hamiltonian, we find similar results. In both cases, our dynamical calculations show no appreciable change in the effects of disorder from that of the initial state of the evolution. We explain our findings in terms the statistics of the disorder in the parameters and the behaviour of the observables with the parameters.